
here \(w_i\in {0,1}\)  and is the decision variable to determine if preventative measures are taken at \(i^{th}\)  stage or not. The goal is to decide which stages \(i\)  action should be taken to make sure \(Z_i\)  does not exceed an upper limit \(U_i\) . \(\Omega _i\)  and \(\Sigma _i\)  are determined by a uniform distribution. We consider the problem setup with Langrangian relaxation [1]}:
\(f({\vec{w}})= -\sum _{i=1}^D\left(cw_i+\frac{\rho }{T}\sum _{k=1}^T1_{\lbrace Z_k>U_i\rbrace }\right) - \lambda ||\vec{w}||_1\) 
